Argument of complex number MCQ - Practice Questions & Answers

JMI B.Tech Application Form 2025: Registration Link, Fees, How to Fill Form

Quick Facts

13 Questions around this concept.

Solve by difficulty

Let w1 be the point obtained by the rotation of z1 = 5 + 4i about the origin through a right angle in the
anticlockwise direction, and w2 be the point obtained by the rotation of z2 = 3 + 5i about the origin through a right angle in the clockwise direction. Then the principal argument of w1 – w2 is equal to :

$\pi-\tan ^{-1} \frac{8}{9}$

$-\pi+\tan ^{-1} \frac{8}{9}$

$\pi-\tan ^{-1} \frac{33}{5}$

$-\pi+\tan ^{-1} \frac{33}{5}$

View Solution

Concepts Covered - 1

Argument of complex number

If a complex number z = x + iy is represented by a point P in Argand plane and OP forms some angle with positive x-axis, let's denote it with ?, then ? is called the argument of z.

$\\\mathrm{\tan\theta=\frac{PM}{OM}}\\\mathrm{\tan\theta=\frac{y}{x}=\frac{Im(z)}{Re(z)}\Rightarrow \theta=\tan^{-1}\frac{y}{x}}\\\mathrm{\arg(z)=\theta=\tan^{-1}\frac{y}{x}}$

If ? lies between -? < ? ≤ ?, then ? is called principal argument. Value of argument differs depending on which quadrant point (x,y) lies.

If it lies in 1^st quadrant then it is ? (acute angle)

If the point lies in 2^nd quadrant, then $arg(z)=\theta =\pi - \tan ^{-1}\frac{y}{|x|}$

So it will be an obtuse +ve angle

If the point lies in lies in 3^rd quadrant then $arg(z)=\theta =-\pi + \tan ^{-1}\frac{y}{x}$

It will be an obtuse -ve angle

If the point lies in 4^th quadrant then $arg(z)=\theta =- \tan ^{-1}\frac{|y|}{x}$

It will be -ve acute angle

Note:

$\\\mathrm{If\;\arg(z)=\frac{\pi}{2}\;\;or\;-\frac{\pi}{2},\;z\;is\;purely\;imaginary.}\\\mathrm{If\;\arg(z)=0\;\;or\;\pi,\;z\;is\;purely\;real.}$

Study it with Videos

Argument of complex number

Study other Related Concepts

Argument of complex number Current Topic

Powers of Iota

Complex number

Algebraic operation on Complex Numbers

Multiplication of Complex Numbers

Conjugates of Complex Numbers

Modulus of complex number and its Properties

Argument of complex number

Polar form of complex numbers

Euler form of complex number

Square root of complex numbers

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Get Answer to all your questions

JMI B.Tech Admission Articles

JMI B.Tech Reservation Criteria 2024 - Check Details Here

Oct 01, 2024

JMI B.Tech Eligibility Criteria 2025 - Check Age Limit, Nationality, Aggregate Marks

Oct 01, 2024

B.Tech/B.Arch Admissions OPEN

Amity University, Noida B.Tech Admissions 2024

Apply

Asia's Only University with the Highest US & UK Accreditation

JSS University Noida Admissions 2024

Apply

170+ Recruiters Including Samsung, Zomato, LG, Adobe and many more | Highest CTC 47 LPA

Atlas SkillTech University | B.Tech Admissions

Apply

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

ITM SLS Baroda University B.Tech Admissions 2024

Apply

Approved by UGC, PCI, & COA. Best Innovative Private Institute in Gujarat. 600+ Recruiters, 3000+ Students Placed, 1500+ Industrial Internship Opportunities, 250+ International Internships.